WLJS Notebook 2.8.1 Preview
f[x_] := 1/x;
v[a_] = Integrate[\[Pi] (*SpB[*)Power[f[x](*|*),(*|*)2](*]SpB*), {x, 1, a}, Assumptions -> a > 1];
s[a_] = Integrate[2 \[Pi] f[x] Sqrt[1 + (*SpB[*)Power[D[f[x], x](*|*),(*|*)2](*]SpB*)], {x, 1, a},
Assumptions -> a > 1];
Manipulate[
Row[{
RevolutionPlot3D[1/s, {s, 1, b},
RevolutionAxis -> {1, 0, 0},
PlotRange -> {{1, 15}, {-1, 1}, {-1, 1}}, Mesh -> None,
ImageSize -> 300, Boxed -> False
],
Plot[{s[x], v[x]}//Evaluate, {x, 1, 16},
ImageSize -> 300,
Epilog->{Orange, PointSize[Large],
Point[{b, v[b] // N}], Blue, Point[{b, s[b] // N}]}
]
}] // Quiet, {{b, 2, "a"}, 1.7, 15}, ContinuousAction->True]
img = ImageResize[ExampleData[{"TestImage","Apples"}], 500];
Manipulate[ImageAdjust[img, i], {i,-1,1,0.3}, ContinuousAction->True]